Types of Sinusoidal Oscillations

1. Damped Oscillations
2. Undamped Oscillations

1. Damped Oscillations-The electrical oscillations whose amplitude goes on decreasing with time are called damped oscillations.

2. Undamped Oscillations- The electrical oscillations whose amplitude remains constant with time are called undamped oscillations.

Oscillatory circuit

A circuit, which produces electrical oscillations of any desired frequency, is known as an oscillatory circuit or tank circuit.

A simple oscillatory circuit consists of a capacitor C and inductance coil L in parallel as shown in figure below. This electrical system can produce electrical oscillations of frequency determined by the values of L and C.

Circuit operations- Assume capacitor is charged from a d. c. source with a polarity as shown in figure 1.

• When switch S is closed as shown in fig.ii, the capacitor will discharge through inductance and the electron flow will be in the direction indicated by the arrow. This current flow sets up magnetic field around the coil. Due to the inductive effect, the current builds up slowly towards a maximum value. The circuit current will be maximum when the capacitor is fully discharged. Hence the electrostatic energy across the capacitor is completely converted into magnetic field energy around the coil.
• Once the capacitor is discharged, the magnetic field will begin to collapse and produce a counter emf. According to Lenz’s law the counter emf will keep the current flowing in the same direction. The result is that the capacitor is now charged with opposite polarity making upper plate of capacitor –ve and lower plate +ve as shown in fig. 3.
• After the collapsing field has recharged the capacitor, the capacitor now begins to discharge and current now flows in the opposite direction as shown in fig. iv.
• The sequence of charge and discharge results in alternating motion of electrons or an oscillating current. The energy is alternately stored in the lectric field of the capacitor C and the magnetic field of the inductance coil L . This interchange of energy between L and C is repeated over and again resulting in the production of Oscillations.

Waveform- In practical tank circuit there are resistive and radiation losses in the coil and dielectric losses in the capacitor. During each cycle a small part of the originally imparted energy is used up to overcome these losses. The result is that the amplitude of oscillating current decreases gradually and eventually it become zero. Therefore tank circuit produces damped oscillations.

Frequency of oscillations- The expression for frequency of oscillation is given by,